who can work this out?

[Ali]

This has me a little stumped, Ive even made it in graph paper, so it isnt a matter of different sized squares. Can anybody explain it to me?

Ali

[cjolley]

If you cut the pieces out very carfuly you will find that they
do not realy match perfectly.
I read about in in M. vos Savant's column in the Parade
Magazine some time ago.
Chuck

[Wombat]

<B>WARNING: Full spoiler! </B>










The hypotenuse of the assembled triangle isn't a straight line. If you look at the dark green triangle and the red triangle, you'll see that they are not similar, and therefore their hypotenuses are not parallel to each other.

On one assembled triangle, the hypotenuse bows out slightly, and the other triangle bows in. The area of this difference amounts to one unit on the grid.

<I>If you can't see that</I>

Taking the bottom left angle of the triangles as the (X,Y) point (0,0), it's easy to compare the two triangles.

The hypotenuse of the bottom triangle intersects the point (5,2), while the top triangle isn't quite big enough to reach that point. The top triangle intersects at (8,3), while the bottom triangle is noticably above that point.

[Ali]

Nope.

Ive cut out all the different shapped bits on graph paper, and re-arranged it, there is an empty square still. It cant be due to the squares being different sizes.

Ali
edit, this was a reply to cjolley

[Ali]

Ah, got it, thanks. My nice little graph cut outs looked so good too.

Thanks

Ali

[Gurm]

I hate stuff like this. I had seen this particular problem before, but those cutouts weren't even on EVEN graph paper. In order for the graph paper to be helpful the squares should all be the same size, no?

- Gurm

[Rags]

Actually the grids are the same size in both pics.

This is the problem, neither one is a triangle, so that's where the problem is. They both have exactly the same surface area colored in.

Do the angles yourself, and you will see they aren't triangles.

Rags

[Gurm]

No no, I see that they aren't triangles. The problem, of course, is that it's HARDER to see when the graph paper isn't even.

- Gurm

[Maggi]

I solved it digitally ...

original shape:

[Maggi]

exchanged shapes, already hinting that there's a discrepancy between both triangles

[Maggi]

overlapping shapes that show the difference in size and finally sum up to the 'missing' square ...

[Greebe]

Oh Maggi go play with your dual XP1800 with 2gigs of mem will ya!

[Maggi]

it's not playing, Greebe ... it's scientific research ...

Cheeze !

[Rags]

Originally posted by Maggi
overlapping shapes that show the difference in size and finally sum up to the 'missing' square ...

You just proved it yourself that they aren't triangles, as such the hypotenuse on one in concave, the other is convex.

Rags

[The PIT]

They're just drunk triangles that all or someones fat just sat on one.